Tracking and following people moving about an environment with a mobile robotic device is an extremely useful task and can be advantageously employed in service robot systems, as well as in so-called party-bot and entertainment-bot systems. In the case of service robots, the mobile robotic device can follow a person moving about his or her home. For example if the person is cleaning or performing home repairs, the robotic device could follow the person while carrying cleaning supplies or tools. Similarly, if the person is incapacitated in some way or elderly, the robotic device could follow that person while carrying medical equipment, medicines, or a communication device—so that these items are readily available no matter where the person is located. Such a service robot could also be helpful in public places, schools and office buildings. In the case of a party-bot, the mobile robotic device could be tasked to follow a person around with a serving tray holding snacks and drinks; or be tasked with capturing video of the person as he or she mingles with guests. In the case of an entertainment-bot, the mobile robotic device could be tasked to follow a person around a venue while playing music or playing a video on a display carried by the robotic device.